http://arxiv.org/abs/2001.01221
This work considers the gravitational $N$-body problem and introduces time-reparametrization functions that allow to define globally solutions of the $N$-body equations. First, a lower bound of the radius of convergence of the solution to the original equations is derived, which suggests an appropriate time-reparametrization. In the new fictitious time $\tau$, it is then proved that any solution exists for all $\tau \in \mathbb{R}$, and that it is uniquely extended as a holomorphic function to a strip of fixed width. As a by-product, a global power series representation of the solutions of the $N$-body problem is obtained. Noteworthy, our global time-regularization remain valid in the limit when one of the masses vanishes. Finally, numerical experiments show the efficiency of the new time-regularization functions for some $N$-problems with close encounters.
M. Antoñana, P. Chartier, J. Makazaga, et. al.
Tue, 7 Jan 20
25/71
Comments: N/A